In a medium saucepan, combine the cranberries, orange juice, water, and orange zest. Bring the mixture to a boil, then reduce the heat and simmer gently for 8 to 10 minutes until the cranberries begin to burst.
Using an immersion blender, potato masher, or blender, carefully blend the mixture until it is mostly smooth. It doesn’t need to be completely smooth, but the smoother the puree, the easier it will be to strain.
Pour the mixture through a fine-mesh sieve into a heatproof bowl. Use a silicone spatula or wooden spoon to press the mixture through the sieve, leaving behind the fibrous bits and seeds from the cranberries and orange zest. Return the strained cranberry sauce to the saucepan.
Place the saucepan over medium-high heat, add the sugar, and stir until it dissolves. Bring the mixture to a boil, stirring often, and continue boiling until the cranberry sauce reaches a temperature between 215°F and 217°F.
Ladle the hot cranberry sauce into sterile canning jars, leaving 1/4-inch of headspace. Wipe the rims clean, place new lids on the jars, and screw the rings on until fingertip tight.
You may store the jars in the refrigerator, or process them for longer storage by placing the jars filled with hot cranberry sauce in a canner. Cover with hot water, bring to a boil, and process for 15 minutes, regardless of whether you use pint, pint-and-a-half, or quart-sized jars.
When finished, turn off the heat and remove the canner lid. Let the jars sit in the water for five minutes before transferring them to a wire rack or towel to cool undisturbed overnight.
Once cool, wipe the jars clean, label them, and store in a cool, dark place for up to one year.